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A168276 a(n) = 2*n - (-1)^n - 1. 4
2, 2, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98, 102, 102, 106, 106, 110, 110, 114, 114, 118, 118, 122, 122, 126, 126, 130, 130 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

FORMULA

a(n) = 4*n - a(n-1) - 4, with n>1, a(1)=2.

from R. J. Mathar, Nov 25 2009: (Start)

a(n) = 2*n - (-1)^n - 1.

a(n) = 2*A109613(n-1).

G.f.: 2*x*(1 + x^2)/((1+x)*(x-1)^2). (End)

a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 16 2013

a(n) = A168277(n)+1. - Vincenzo Librandi, Sep 17 2013

E.g.f.: (-1 + 2*exp(x) + (2*x -1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

MATHEMATICA

CoefficientList[Series[2 (1 + x^2) / ((1 + x) (x - 1)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 16 2013 *)

Table[2 n - 1 - (-1)^n, {n, 70}] (* Bruno Berselli, Sep 17 2013 *)

LinearRecurrence[{1, 1, -1}, {2, 2, 6}, 70] (* Harvey P. Dale, Oct 22 2014 *)

PROG

(MAGMA) [2*n-1-(-1)^n: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013

CROSSREFS

Cf. A039722, A168277.

Cf. A063210. [R. J. Mathar, Nov 25 2009]

Sequence in context: A151888 A320046 A289835 * A039722 A237363 A082542

Adjacent sequences:  A168273 A168274 A168275 * A168277 A168278 A168279

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 22 2009

EXTENSIONS

Replaced the previous definition with the closed form. - Bruno Berselli, Sep 17 2013

STATUS

approved

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Last modified February 16 15:17 EST 2020. Contains 331961 sequences. (Running on oeis4.)